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Maximum theorem

The maximum theorem provides conditions for the continuity of an optimized function and the set of its maximizers with respect to its parameters. The statement was first proven by Claude Berge in 1959. The theorem is primarily used in mathematical economics and optimal control.

Examples, Statement of theorem & Variants and generalizations

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Examples

Utility maximization problemUtility functionBudget setIndirect utility functionMarshallian demand
8 related topics

Statement of theorem

ProductCorrespondenceHemicontinuous
3 related topics

Variants and generalizations

QuasiconcaveConcaveConvex
3 related topics

Proof

Open setExtreme Value theorem
2 related topics

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Overview

Statement of theorem

Proof

Variants and generalizations

Examples

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Maximum theorem

Nodes27
Edges26
Triples5
Avg. degree1.93
Density0.074074
Components1

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Maximum theorem

Top relations

related to Statement of theorem · 3
Maximum theorem → Define, Let, Theta
is a · 1
Maximum theorem → result of combining two independent theorems together.Theorem 1
related to Variants · 1
Maximum theorem → The

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Important terminology

displaystyle theta function theorem continuous set correspondence hemicontinuous maximum upper nonempty conditions continuity correspondences mathbb compact-valued value compact maximizers utility

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Maximum theoremis aresult of combining two independent theorems together.Theorem 10.90text
Maximum theoremrelated to Statement of theoremLet0.60section
Maximum theoremrelated to Statement of theoremTheta0.60section
Maximum theoremrelated to Statement of theoremDefine0.60section
Maximum theoremrelated to VariantsThe0.60section

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